Quadratic Formula
Quadratics come in this form:
ax 2 + bx + c = 0
Sometimes it is factorable and finding
the value(s) of x is easy. What do ...
2 + bx + c = 0
ax

   2 + bx + c = 0
ax
a      a     a    a


  2
x     + bx       +c=0
        a         a
x 2
                  + bx       +c=0
                    a         a

          x 2
                 + bx        =0-c
   ...
2                   2
(   x+   b
         2a
           )    =    -c +
                      a     ( )
                   ...
2
                     ( )
x+ b     =±   -c +    b
  2a          a       2a



                    2
x   =±   -c +
       ...
2
x=   ±   -c +
          a
                ( )b
                   2a
                           -   b
                  ...
2
x= -
                          ( )
         b ± 2a    -c +    b
         2a  2a     a      2a


                        ...
2
                               ( )
x=   -       b ± 2a     -c +       b
                         a         2a
          ...
2       2      2
x=   -   b ±   - c (2a) +
                 a           ( )
                              b
              ...
2       2         2
x=   -   b ±   - c 4a +
                 a        ( )
                          b
                    ...
2     2            2
x=   -       b ±   - c 4a +
                     a        ( )
                              b
       ...
2
x = -b ±    b - 4ac
           2a
2
   7x + 14x - 3 = 0

What are the roots of
the above function

               2
  x = -b ±    b - 4ac
             2a

 ...
2
  7x + 14x - 3 = 0

             2
x = -14 ± 14 - 4(7)(-3)
         2(7)


x = -14 ± 196 + 84
         14
x = -14 ± 280
         14


x = -14 ± 16.73
         14
x = -14 ± 16.73
                     14

x1 = -14 + 16.73       x2 = -14 - 16.73
          14                     14
x1 = ...
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March 9 Quadratic Formula

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March 9 Quadratic Formula

  1. 1. Quadratic Formula
  2. 2. Quadratics come in this form: ax 2 + bx + c = 0 Sometimes it is factorable and finding the value(s) of x is easy. What do you do when it isn't factorable? Can you still solve for x?
  3. 3. 2 + bx + c = 0 ax 2 + bx + c = 0 ax a a a a 2 x + bx +c=0 a a
  4. 4. x 2 + bx +c=0 a a x 2 + bx =0-c a a 2 2= 2 x + bx + a ( ) b 2a -c + a ( ) b 2a
  5. 5. 2 2 ( x+ b 2a ) = -c + a ( ) b 2a 2 2 ( x+ b 2a ) = -c + a ( ) b 2a 2 ( ) x+ b =± -c + b 2a a 2a
  6. 6. 2 ( ) x+ b =± -c + b 2a a 2a 2 x =± -c + a ( ) b 2a - b 2a
  7. 7. 2 x= ± -c + a ( )b 2a - b 2a 2 x= - ( ) b ± -c + b 2a a 2a 2 x= - ( ) b ± 2a -c + b 2a 2a a 2a
  8. 8. 2 x= - ( ) b ± 2a -c + b 2a 2a a 2a 2 ( ) x= - b ± 2a -c + b a 2a 2a
  9. 9. 2 ( ) x= - b ± 2a -c + b a 2a 2a 2 2 2 x= - b ± - c (2a) + a ( ) b 2a (2a) 2a
  10. 10. 2 2 2 x= - b ± - c (2a) + a ( ) b 2a (2a) 2a 2 2 2 x= - b ± - c 4a + a ( ) b 4a 2 4a 2a
  11. 11. 2 2 2 x= - b ± - c 4a + a ( ) b 4a 2 4a 2a 2 2 2 x= - b ± - c 4a + a ( ) b 4a 2 4a 2a
  12. 12. 2 2 2 x= - b ± - c 4a + a ( ) b 4a 2 4a 2a 2 x= - b ± - c 4a + b 2a
  13. 13. 2 x = -b ± b - 4ac 2a
  14. 14. 2 7x + 14x - 3 = 0 What are the roots of the above function 2 x = -b ± b - 4ac 2a 2 7x + 14x - 3 = 0
  15. 15. 2 7x + 14x - 3 = 0 2 x = -14 ± 14 - 4(7)(-3) 2(7) x = -14 ± 196 + 84 14
  16. 16. x = -14 ± 280 14 x = -14 ± 16.73 14
  17. 17. x = -14 ± 16.73 14 x1 = -14 + 16.73 x2 = -14 - 16.73 14 14 x1 = 2.73 x2 = -30.73 14 14 x1 = .2 x2 = -2.2

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